Question

A circle has a circumference of 28 centimeters. If an arc subtends a central angle of 55 degrees, what is the arc length?

Answer 1

Answer:

s = 4.28 cm (Answer A)

Step-by-step explanation:

1) The formula for the circumference of a circle of radius r is C = 2(pi)r, and this corresponds to a full circle, with central angle 360 degrees.  

2) Here the circumference is 28 cm.  Therefore, solving for the radius involves the following calculation:   28 cm = 2(pi)r, or

r = (28 cm) / (2 pi), or (28 cm) / 6.28 = 4.46 cm.  

3) The arc length s = r(theta), when the central angle (theta) is 55 degrees, is (55/360) times the circumference of the circle:  (55/360)(28 cm), or

s = 4.28 cm (Answer A)